Javi Gracia’s sacking was confirmed earlier today with Allardyce brought in for the last four Premier League games of the campaign.
Leeds have lost five of their last six Premier League games and are sitting just above the relegation zone owing to a superior goal difference.
Many believe Leeds are sleepwalking to relegation as they are set to play Manchester City, Newcastle United, West Ham and Tottenham in their last four league games.
However, Palmer believes Allardyce will do enough to keep Leeds in the Premier League this season.
The former White feels that they need only one win to survive given the way the bottom of the table has been shaping up ahead of the last few weeks of the season.
Palmer said on talkSPORT: “I think he will do it.
“One win will be good enough to do it.
“What killed the teams at the bottom the other night was Leicester and Everton drawing, one of the teams needed to win to give them a chance.
“I can only see Forest getting three points at home to Southampton, I can’t see them getting any more points in the other games.
“So, I think Sam will do it.”
Former Leeds striker Robbie Keane has joined Allardyce as part of his coaching staff for the last four games.
